Mathematics, as an expression of human thinking, embodies people's aggressive will, meticulous logical reasoning and pursuit of perfection. I brought you a math manuscript below. Let's have a look.
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Contents of Mathematical Manuscripts 1: A Complete Collection of Mathematical Formulas in Primary Schools
1, additive commutative law: Two numbers are added to exchange the position of addend, and the sum is unchanged.
2. Law of addition and association: When three numbers are added, the first two numbers are added first, or the last two numbers are added first, and then the third number is added, and the sum is unchanged.
3. Multiplication and exchange law: when two numbers are multiplied, the position of the exchange factor and the product remain unchanged.
4. Multiplication and association law: When three numbers are multiplied, the first two numbers are multiplied, or the second two numbers are multiplied first, and then the third number is multiplied, and the product remains unchanged.
5. Multiplication and distribution law: When two numbers are multiplied by the same number, you can multiply the two addends by this number respectively, and then add the two products, and the result remains unchanged.
6. Nature of division: In division, the dividend and divisor are expanded (or reduced) by the same multiple at the same time, and the quotient remains unchanged. Divide 0 by any number other than 0 to get 0.
Simple multiplication: Multiplied by 0 at the end of the multiplier. You can multiply 1 before 0, and 0 does not participate in the operation. Drop a few 0s at the end of the product before adding.
7. What is an equation? An equation in which the value on the left of the equal sign is equal to the value on the right of the equal sign is called an equation.
Basic properties of the equation: When both sides of the equation are multiplied (or divided) by the same number at the same time, the equation is still valid.
8. What is Equation A: An equation with an unknown number is an equation.
9. What is a linear equation with one variable? A: A linear equation with an unknown number and an unknown degree.
Example method and calculation of learning linear equation of one variable. That is, an example is given to illustrate that the formula is replaced by χ and calculated.
10, fraction: divide the unit "1" into several parts on average, and the number representing such a part or points is called a fraction.
1 1, addition and subtraction of fractions: add and subtract fractions with denominator, only add and subtract numerators, and the denominator remains unchanged. Fractions of different denominators are added and subtracted, first divided, then added and subtracted.
12, comparison of fractional size: Compared with the fraction of denominator, the numerator is large and the numerator is small.
Compare the scores of different denominators, divide them first and then compare them; If the numerator is the same, the denominator is big and small.
13, the fraction is multiplied by the integer, and the product of the numerator of the fraction multiplied by the integer is the numerator, and the denominator remains unchanged.
14, the fraction multiplied by the fraction, the product multiplied by the numerator is the numerator, and the product multiplied by the denominator is the denominator.
15, the fraction divided by an integer (except 0) is equal to the fraction multiplied by the reciprocal of this integer.
16, true fraction: numerator is less than denominator. A score is called a true score.
17. False fraction: the fraction with numerator greater than denominator or numerator equal to denominator is called false fraction. False score is greater than or equal to 1.
18, with fraction: write false fraction as integer and true fraction, which is called with fraction.
19, the basic nature of the fraction: the numerator and denominator of the fraction are multiplied or divided by the same number at the same time (except 0), and the size of the fraction remains unchanged.
20, a number divided by a fraction is equal to the number multiplied by the reciprocal of the fraction.
Content 2 of Mathematical Manuscripts: Mathematical Stories
A famous mathematical figure-Cantor's short story
Because the study of infinity often leads to some logical but absurd results (called "paradox"), many great mathematicians are afraid of falling into it and adopt an evasive attitude. During the period of 1874- 1876, Cantor, a young German mathematician less than 30 years old, declared war on the mysterious infinity. With hard sweat, he successfully proved that points on a straight line can correspond to points on a plane one by one, and can also correspond to points in space one by one. In this way, it seems that there are as many points on the 1 cm long line segment as there are points in the Pacific Ocean and the whole earth. In the following years, Cantor published a series of articles about this kind of "infinite set" and drew many amazing conclusions through strict proof. Cantor's creative work has formed a sharp conflict with the traditional mathematical concept, which has been opposed, attacked and even abused by some people. Some people say that Cantor's set theory is a kind of "disease", Cantor's concept is "fog in fog", and even Cantor is a "madman". Great mental pressure from the authority of mathematics finally destroyed Cantor, making him exhausted, suffering from schizophrenia and being sent to a mental hospital.
True gold is not afraid of fire, and Cantor's thought finally shines. At the first international congress of mathematicians held in 1897, his achievements were recognized, and Russell, a great philosopher and mathematician, praised Cantor's work as "probably the greatest work that can be boasted in this era." But at this time, Cantor was still in a trance, unable to get comfort and joy from people's reverence. 1918 65438+1October 6th, Cantor died in a mental hospital.
Content 3 of Mathematical Manuscripts: The Origin of Mathematical Symbols
Besides counting, mathematics needs a set of mathematical symbols to express the relationship between number and number, number and shape. The invention and use of mathematical symbols are later than numbers, but they are much more numerous. Now there are more than 200 kinds in common use, and there are more than 20 kinds in junior high school math books. They all had an interesting experience.
For example, there used to be several kinds of plus signs, but now the "+"sign is widely used.
+comes from the Latin "et" (meaning "and"). /kloc-in the 6th century, the Italian scientist Nicolo Tartaglia used the initial letter of "più" (meaning "add") to indicate adding, and the grass was "μ" and finally became "+".
The number "-"evolved from the Latin word "minus" (meaning "minus"), abbreviated as m, and then omitted the letter, it became "-".
/kloc-In the 5th century, German mathematician Wei Demei officially determined that "+"was used as a plus sign and "-"was used as a minus sign.
Multipliers have been used for more than a dozen times, and now they are commonly used in two ways. One is "x", which was first proposed by British mathematician orcutt on 163 1; One is "",which was first created by British mathematician heriott. Leibniz, a German mathematician, thinks that "×" is like the Latin letter "X", so he opposes it and agrees to use "×". He himself proposed to use "п" to represent multiplication. But this symbol is now applied to set theory.
Content 4 of Mathematical Manuscripts: Mathematical Jokes
When Xiao Ming came back, his mother asked him how he did in the elementary school math exam. Xiao Ming said: "I can basically do it, but I can't do a problem of 3 times 7." Finally, when the bell rang, I wrote 18 regardless of the willy-nilly. "
Grandma: "What is 1+2?"
Grandson: "equal to 3."
Grandma: "That's right, so you'll get 3 pieces of candy."
Sun Tzu: "If I had known this, I would have said it was equal to 5!" " "
Content 5 of Mathematical Manuscripts: Mathematicians in Animals
Honeycomb is a strictly hexagonal cylinder, with a flat hexagonal opening at one end and a closed hexagonal diamond bottom at the other end, which consists of three identical diamonds. The rhombic obtuse angle of the chassis is 109 degrees 28 minutes, and all acute angles are 70 degrees 32 minutes, which is both firm and material-saving. The honeycomb wall thickness is 0.073 mm, and the error is very small.
Red-crowned cranes always move in groups, and they are arranged in the word "people". The angle of the herringbone is 1 10 degrees. More accurate calculation also shows that the angle of the herringbone is half-that is, the angle between each side and the direction of the crane group is 54 degrees, 44 minutes and 8 seconds! And the angle of diamond crystal is exactly 54 degrees, 44 minutes and 8 seconds! Is it a coincidence or some "tacit understanding" of nature?
Spider's "gossip" net is a complex and beautiful octagonal geometric pattern, and it is difficult for people to draw a symmetrical pattern like a spider even with rulers and compasses.
In winter, when a cat sleeps, it always hugs its body into a ball. There is also mathematics in it, because the shape of the ball minimizes the surface area of the body, so it emits the least heat.
The real "genius" of mathematics is coral. Coral writes a "calendar" on its body, and "draws" 365 stripes on its wall every year, apparently one a day. Strangely, paleontologists found that corals 350 million years ago "painted" 400 watercolors every year. Astronomers tell us that at that time, the earth only had 2 1.9 hours a day, not 365 days a year, but 400 days.
Mathematical Manuscript Content 6: Mathematical Brainstorming
The age of the owner
You have a ship carrying 15 crew, 60 passengers and 300 tons of cargo. You can according to the above.
Show, calculate the age of the host?
Three goddesses
Three goddesses sat in an ancient Indian temple.
Their names are truth, lies and wisdom. They have the following conversation.
The one on the left asked, "Who is sitting next to you?"
"The truth," she replied. The middle one asked, "Who are you?"
"Wisdom," she answered.
Now it is clear who is who.
Mathematical Manuscript Content 7: Mathematical Famous Words
Russell said, "Mathematics is symbol plus logic."
Pythagoras said, "Numbers dominate the universe."
Halmos said, "Mathematics is a unique art."
Misra said: "Mathematics is the highest achievement of human thinking."
Bacon (English philosopher) said, "Mathematics is the key to science."
Bourbaki School (a French mathematical research group) holds that "mathematics is a theory to study abstract structures".
Hegel said: "Mathematics is the symbol that God describes nature."
Oscar Wilde (president of the American Mathematical Society) said: "Mathematics is a culture that will continue to evolve."
Plato said, "Mathematics is the highest form of all knowledge."
Court said: "Mathematics is the brightest pearl in the crown of human wisdom."
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